If a product is wheat free, does that mean it is gluten free? Is oat flour ok?

Simply put, no and no. Wheat free many times will still have barley or oats. Some consider oats okay but the processing of oats make them extrememly risky and most of us avoid them.

since the gluten that harms celiacs is found in wheat, barley, rye, and possibly oats, you can see that just being free of wheat is *NOT* enough to be safe. oats are a different ball of wax - commercial ones are contaminated, and even if you buy specifcally gluten free ones from the handful of farms that grow them that way (yes, it's different), about 10% of celiacs react to oats as well.